where the constant \(C\)  is a fitting parameter, \(D^{\rm {rough}}\)  is the
self-diffusivity of the fluid between the rough surface of interest,
and \(D^{\rm {ref}}\)  is the self diffusivity of the fluid at an
appropriately chosen reference state under the same thermodynamic
conditions. We note that
Eq. (REF ) has, to first order, the same dependence
on \(H\)  as the self-diffusivity of a Brownian particle in the center of a
slit-pore.[1]} This, in fact, was the
inspiration for the functional form chosen in Eq. (REF ).
For the thermal walls, we take
\(D^{\rm {rough}}=D^{\rm {TW}}\)  and \(D^{\rm {ref}}=D^{\rm {SW}}\) , and
we find that \(C \approx 1.44\sigma \) .
